1. Chapter 7: Beyond Black-Scholes

2. Black-Scholes Model for vanilla options

3. Implied volatility and volatility smile

4. Continued

5. Improved models Local volatility model Stochastic volatility model
Jump diffusion model
Others: discrete hedging, transaction cost

6. Local volatility model

7. A special case:
Identification of

8. How to use the local volatility model
Calibration of the model: Identify the volatility function from the market prices of vanilla options
Price non-traded contracts by using the model

9. Stochastic volatility model

10. Pricing model

11. Continued

12. The Market Price of Risk

13. Risk neutral processes

14. Derivatives on a single underlying variable

15. Pricing equation

16. Two Named Models
Hull White
Heston

17. Example 1: Hull-White model

18. Example 2: Heston Model

19. Jump-diffusion model
Poisson process

20. Jump-diffusion Process

21. Hedging

22. Ito Lemma

23. Merton’s Model (1976)
Jump risks are diversified

24. Summary: purpose
Understand the market better
Price options at the OCT market

25. Beyond the Black-Scholes World
Local volatility model
Stochastic volatility model
Jump diffusion model

26. Parameters , J Local volatility model: =(S,t)
Stochastic volatility model:
Hull-White model (3 parameters)
Heston model (2 parameters)
Jump diffusion model
, J